The length of a rectangle is three less than twice the width. The perimeter is 106cm. Find the length and the width.

L = 36.33333333 ...

w = 16.6666666666 ...

Step-by-step explanation:

lets call the width "w" and the length "L"

L = 2w + 3 (because the length is three less, so W+3, than twice the width, so 2w)

2w + 2L = 106 (because a perimeter of a rectangle is the 2 lengths and 2 widths)

2w + 2 (2w+3) = 106 (because we know L=2w-3, we just sub that in)

2w+4w+6 = 106 (we expand the brackets by multiplying 2w-3 by 2)

6w+6 = 106 (put 4 and 3 together)

6w = 100 (move + 6 to the other side, so it becomes 106-6 which is 112)

w = 100/6 which is also 16.66666

then we put this into the original formula (2w+3)

L = 200/6 + 3 (because you sub in what we got for w, so 100/6*2, which is 200/6)

L = 36.33333333 ...